I want to hire a tour guide services only for a few hours in the old city of Jerusalem.

Next to the tourists information centre there are always these guys offering their services, but from what I understand they are not authorised guides. I've been to Jerusalem several times and I always see them there...

So, how can I find a guide that is authorised and will agree to guide us just for 2-3 hours? (All the Via Dolorosa and Holy Sepulchre)

You are absolutely writ for not using unauthorized tour guide. At the Jaffa gate you can have a free tour in the old city. The tourguides are government licensed. They do A good job and expecting to get A tip.